What is Volume: Definition and 1000 Discussions

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or 3D shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.
Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, and circular shapes can be easily calculated using arithmetic formulas. Volumes of complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.
The volume of a solid (whether regularly or irregularly shaped) can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater than the volume of just one of the substances. However, sometimes one substance dissolves in the other and in such cases the combined volume is not additive.In differential geometry, volume is expressed by means of the volume form, and is an important global Riemannian invariant.
In thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure.

View More On Wikipedia.org
Recent contents Top users
  1. K

    Control volume, Fluid mechanics

    Homework Statement I have a situation as illustrated by the image above, where the red box illustrates the CV. The pressure on the left side of CV is P1, while the pressure on the right side of CV is P2. Here I´ve directed the pressure forces acting inwards on CV. The problem arises with Fk. I...
  2. bornofflame

    [MultiVarCalc] Find the volume of the solid

    Homework Statement Find the volume of the solid between the cone ##z = \sqrt{x^2 + y^2}## and the paraboloid ##z = 12 - x^2 - y^2##. Homework Equations ##x^2 + y^2 = r^2## The Attempt at a Solution I drew a simple diagram to start off with to visualize the solid formed by the intersection of...
  3. thevinciz

    How do I find the volume of gas using the given mass of oxygen?

    Homework Statement Homework EquationsThe Attempt at a Solution I have tried to change mass of oxygen into mol and I got ratio of oxygen and nitrogen. And I don't really know what to do.
  4. karush

    MHB T.15.28 Find the volume of the region

    $\tiny{t.15.28}$ $\text{Find the volume of the region bounded above by the surface }\\$ $\text{$z=4-y^2$ and below by the rectangle $R: 0 \ge x \ge 1 \quad 0\ge y \ge 2$.}$ $\begin{align*}\displaystyle I&=\iint \limits_{R}4-y^2 \, dA&(1)\\ &=\int_{0}^{2}\int_{0}^{1}4-y^2 \, dxdy...
  5. K

    Heat transfer in a fin with constant volume

    Assume we have a cylindrical fin which has the effective length of L and its efficiency is given by the equation: $$η=exp(-0.32mL)$$ where $$m=\sqrt{\frac{hP}{kA}}$$ where P is perimeter and A is the cross sectional area of the fin. If the volume of the fin remains constant, which of the...
  6. N

    A Volume of 3-Torus: Formula and Calculations

    I have recently read that physicists are exploring the possibility that the universe is a 3-torus. I have been trying to find the formula for the volume of a three-torus online but cannot find it. Can anyone tell me the formula?
  7. J

    Motion of point when sound volume goes up

    Homework Statement A radio speaker produces sound when a membrane called a diaphragm vibrates, as shown above. A person turns up the volume on the radio. Which of the following aspects of the motion of a point on the diaphragm must increase? a) the max. displacement only b) the average...
  8. Irl495

    Minimum gas pressure to measure its volume with an eudiometer

    Hello, As you can see in the attached hand drawing+calculation, my question concerns the typical method of evolved gas volume measurement by water displacement in an inverted graduated cylinder or "eudiometer". Once a bubble (cavity to be precise) of gas leaves the end of the tube through...
  9. I

    1 volume of hydrogen = how many hydrogen molecules there?

    ''1 volume of hydrogen + 1 volume of hydrogen + 1 volume of oxygen = 2 volumes of water vapor'' Now my questions are as follows: 1. How many hydrogen molecules in 1 volume of hydrogen? 2. How many oxygen molecules in 1 volume of oxygen? 3. how many water vapor molecules in 2 volumes of water...
  10. R

    Harmonic Oscillator and Volume of Unit Cell in Phase Space

    Long time no see, PhysicsForums. Nevertheless, I have gotten myself into a statistical mechanics class where the prof is pretty brutal and while I can usually manage, this problem finally has me stumped. I'd like to be nudged in the right direction, not outright given the answer if possible. I...
  11. T

    Volume of a sphere in Schwarzschild metric

    Homework Statement Calculate the volume of a sphere of radius ##r## in the Schwarzschild metric. Homework Equations I know that \begin{align} dV&=\sqrt{g_\text{11}g_\text{22}g_\text{33}}dx^1dx^2dx^3 \nonumber \\ &= \sqrt{(1-r_s/r)^{-1}(r^2)(r^2\sin^2\theta)} \nonumber \end{align} in the...
  12. X

    A Comoving distance, causality volume and entropy

    Hello everyone ! I try to find the expression of the time derivative of the entropy for the CMB (photon gas) but I am stuck with the calculations. We are in the matter-domination area and at the present time (Ro=1). No radiation and no vacuum, only the curvature. The different equations are...
  13. E

    Increase in the volume of a sound

    Homework Statement A person turns up the volume on a radio. Which aspects of the motion of a point on the diaphragm must increase? a. maximum displacement only b. average speed only c. both maximum displacement and average speed d. neither maximum displacement nor average speed Homework...
  14. R

    Find volume of the solid

    Homework Statement Find volume of the solid that lies above the cone Φ = π/3 and below the sphere ρ = 4cosΦ Homework EquationsThe Attempt at a Solution Obviously this is a triple integral. My book tells me that 0 ≤ρ≤ 4cosΦ but this makes no sense to me. From the problem, it lies ABOVE the...
  15. A

    MHB Volume of 4 intersecting cylinders

    Hello.Can you please help me find an expression for the volume of the left body which is actually 4 cylinders with diameter = D placed on the vertices of the cube with side length L (the cylinders are being "cut" by the corners of the cube). Thank you!
  16. Richie Smash

    B Why is the volume of a gas bigger during a phase change

    Hello, I would like to know, why is the volume of gas produced during phase change significantly more than the original volume of the liquid being used? Say water changing phase at 1atm.
  17. C

    Finding volume of one compound using Stoichiometry equation

    Homework Statement I am having a problem finding the volume of one compound while having the molarity and volume for another using a balanced equation. This is the problem statement: What volume in mL of ammonium carbonate is needed to react completely with 200.0 mL of 1.500 M silver (I)...
  18. J

    Van der Waals EOS using reduced molar volume

    Homework Statement I'm taking an online PChem course where the instructor throws out Z = 3Vr/(3Vr – 1) – 9/(8 VrTr); where Vr is the reduced molar volume. 2. Homework Equations {P + a/Vm^2}{Vm – b} = RT; where Vm is the molar volume Tc = 8a/27Rb ; Vc = 3b ; Pc = a/27b^2 3. The Attempt...
  19. J

    Pressure and Volume Relationship in Closed Bottles

    Homework Statement I have two closed bottles one has a smaller volume that the other. (initially atmospheric pressure in both and then closed with a cap) If I heat both bottles up, which one will increase in pressure more the larger bottle or smaller one. Homework Equations PV=nRT ? The...
  20. D

    MHB (Integration) Find volume using disk method when rotated about the X-axis

    x = 2y - y2 x = y
  21. K

    Sound volume (life experience)

    I live in a country where people (unfortunately) have a culture of listening music at very high volume in their houses, frequently from their car. However I've been noticing that the sound some of the neighbours sound oscillates from time to time between a high volume and a "low" volume. I've...
  22. P

    Volume of water in a container

    Homework Statement A closed container is connected with a tube, water will enter the container via this tube. How would the amount of water in the container affect the pressure in it when water enters the container via the tube? Is this the same as changing the volume of the container (which...
  23. A

    Uncertainty/error of a volume is greater than the normal volume

    Homework Statement I have an empty cylinder with an external diameter of (23.0 ± 0.5) mm, an internal diameter of (22.5 ± 0.5) mm and a height of (60.0 ± 0.5) mm. I need to calculate its volume with its uncertainty/error. Homework Equations The Attempt at a Solution I do it like this...
  24. F

    Find the volume using the shell method

    Homework Statement Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y = x + 2 and the parabola y=x^2 about the x- axis. Homework Equations - The Attempt at a Solution 1) x = √ (y) 2) x= y -2 V = ∫ (2 π ) ( y ) ( √ (y) - y + 2 ) from 0...
  25. B

    Compression and Expansion of a Volume of Air

    Homework Statement Air with an initial volume of 0.12m³, pressure 1 bar and temperature 18°C is compressed according to the law pV1.3 = c through an 8:1 compression ratio. It is then allowed to expand isothermally back to its initial volume. Determine: i) the pressure and temperature after...
  26. A

    What is the volume of a block of silver that weighs 107 N

    How to find the volume of a block of silver that weighs 107 Newtons
  27. F

    Electric Flux in a Closed Space: Volume, Area & Benefits

    I believe the electric flux within a closed space can be found with the equation phi = Q/ε0. Can this be used for volume and area, or just volume? Also what good does this do. Why would I want to know the electric flux of something?
  28. E

    Why is internal energy not a function of pressure?

    I'm reading a book on thermal physics and the author says this: "In general, the internal energy will be a function of temperature and volume, so that we can write U =U(T,V) " How do we know this intuitively and how do we know that internal energy is not a function of pressure as well?
  29. A

    MHB How to find volume of cone+hemisphere on the cone using spherical coordinate

    i have a problem about find volume of hemisphere I do not know the true extent of radius r (0 to ?) i think... cone ( 0 < r < R cosec(\theta) ) hemisphere (0 < r < R)
  30. orangeraindrops

    What does the area under a volume vs time graph represent?

    Homework Statement I have a function showing the volume of water in a bay at different times in the day, and I want to know what the area under this curve would represent (if it represents anything meaningful). I know how to integrate, so that isn't a problem. Homework Equations I am...
  31. D

    Integration for the Volume of an Ellipsoid

    Homework Statement Let E be the ellipsoid x^2 + 2xy +5y^ +4z^2 = 1 Find the Volume of E Homework Equations None, just various integration methods. The Attempt at a Solution I know we're not supposed to say 'I don't know where to start' but with this one I really don't. If the best approach...
  32. Another

    How to find the volume of a hemisphere on top of a cone

    Volume of hemi-sphere = ∫ ∫ ∫ r2 sinθ dr dθ dφ i thing (r < r < (r + R)cosθ ) ( 0 < θ < 60 = π/6) and ( 0 < φ < 2π) integral = 2π ∫ ⅓r3 sin θ dθ = 2π ∫ ⅓ [((r+R)cosθ)3 - r3] sin θ dθ i don't know how to find volume of hemi-spere
  33. Another

    How to find the volume of a sphere [spherical coordinates]

    i don't know to using limit of r ?
  34. B

    Volume, pressure and final temperature

    Homework Statement a) A mass of 0.12 kg of air has an initial temperature of 500°C and pressure 0.8 MPa. If the air is expanded according to the law pV1.2 = c to a final volume of 90 litres, determine i) its initial volume, ii) its final pressure, iii) its final temperature...
  35. lc99

    Volume using Archimedes Method

    Homework Statement Homework Equations Volume of Sphere = 4/3 pi r^3 d = m/v The Attempt at a Solution my attempt is: r = 2 Vsphere = 32/3 pi cm^3 density of mercury = 13.53 g/ml d*v of sphere = 259.7grams 259.7 grams of sphere * (1/density of mercury) = 259.7g *( 1 ml / 13.53 g) = 19.2 ml...
  36. K

    Pitch and amplitude of sound wave Vs its volume

    Hi. If I know the pitch and amplitude of a sound wave, will I be able to calculate its volume. I can understand volume of devices vary betwerb brands and other categories. For the sake of discussion, let's assume volume to be a consistent unit or if db is the right unit, let's take that.
  37. C

    MHB Partial Volume of a Cylinder Calculation

    It's been a long time since I've attended school, over 33 years ago. So my question may seem basic to many here. I wish to calculate the partial volume of a cylinder for my excel spreadsheet project. The formula I've found is attached. (unable to type it) But I do not fully understand this...
  38. Z

    MHB Calculating Sphere Volume Cut by 2 Planes & Angle "e" & Distance "a

    I want to calculate the volume of a sphere cut by two arbitrary plane. There is a intersection angle between these two planes, which is not 90 degrees. One of these two planes is fixed and located on plane "x-o-y", and the other is perpendicular to plane "x-o-z" and moves the distance "a" from...
  39. M

    Liquid volume loss during pressure test

    Hi, I'm doing a pressure test with a liquid medium. I have a fixed volume and I know the pressure drop, and temperature change - how do I calculate volume of liquid lost in a leak?
  40. Richie Smash

    Find volume of pesticide after pressure decreases

    Homework Statement Here is a pesticide spray vessel, of total volume of 10 litres, containing 8 litres of pesticide. Valve B is closed first,and the space above the air is filled with air at a pressure of 200KPa until the desired pressure is reached, and then valve A is then closed. The...
  41. R

    Time to warm a volume of air to room temperature in a container

    Positing an empty container, underground, with a static temperature of 50F (both container, earth, and air temperature) and a volume of X... and introducing (and displacing) into this container a parcel of 30F air of volume Y (which is less than the volume of X)... Is there any way to...
  42. nightingale123

    I N-th dimensional Riemann integral

    Hello I have a question regarding something we wrote in class today. Let ##A## be a bounded subset of ##R^n##, let ##f,g:A\to \mathbb{R}## be integrable functions on A. ##a)## if ## A## has a volume and ##\forall x \in A :m\leq f(x) \leq M## then ##mV(A)\leq \int_{A}f(x)\leq MV(A)## this...
  43. S

    Why does polarizability have units of volume?

    Not sure if I'm posting in the wrong place.
  44. E

    How long to heat a given volume of air?

    Homework Statement I am working on a problem where I need to determine the time taken for an air heater with an 8kW output to heat a volume of air of 9m^3 by 25C. I am neglecting all losses at the moment. It almost seems too simple in my mind that I'm concerned I'm overlooking...
  45. gasar8

    How Does Deformation Affect Surface and Volume Elements on a Sphere?

    Homework Statement Show that the surface and volume element on a deformed sphere are \sigma = \frac{\rho^2 \sin \theta}{\cos \gamma} d\phi d\theta, dV = \rho^3 \sin \theta d\phi d\theta, if \gamma is the angle between normal vector and radius vector. Homework Equations n\cdot r = \cos...
  46. ElectricRay

    Relation between pressure and volume when heating a gas

    Hi all, A happy 2018 for all PF members. I have a question. I am trying to understand some basic principle of thermodynamics. My book tells me tge following: "Heating of a gas at a constant pressure uses more heat as when heating the same gas a constant volume" How do i interpret this? I...
  47. F

    Molar volume and surface tension of nanoparticle

    Hi .how can i calculate the molar volume and surface tension of nanoparticles ? shoud i have to calculate? or these parameters is available in tables or sth?
  48. K

    Can't understand how flow work is possible in a control volume

    I am struggling to fully grasp the concept of flow work for a non-deformabable control volume. Nearly every source puts it in this way: flow work is the work required to push fluid into and out of the control volume and as such is defined as Pv on a unit mass basis. But how can this work be...
  49. HelloCthulhu

    Floating Water Bridge and Dielectric Strength per Volume

    I recently watched a great video demonstrating the floating water bridge experiment: At around 34 sec, you can see an electrostatic discharge before the water bridge forms. I've read that this is due to the electrostatic breakdown of air between the two beakers.This made me curious about the...
  50. Pushoam

    Free energy per unit volume of an ideal gas

    Homework Statement Homework EquationsThe Attempt at a Solution [/B] I am taking the free energy as the internal energy of the ideal gas. Then the average internal energy per unit volume is ## \frac { 3 nk_B T } {2 } ##. So, the correct option is (c). Is this correct?
Back
Top